# S&P 500

## Can Low Rates Explain High Stock Prices? Not So Fast. -- Journal Report

By Mark Hulbert

Today's low interest rates justify above-average price/earnings ratios. That's the theory, anyway. Unfortunately, that theory doesn't hold up when you look at it through the lens of history.

The S&P 500's current P/E is well above its long-term average. It is 21.8 when calculated using trailing as-reported earnings, which is 39% higher than the average since 1871 of 15.7. In the absence of mitigating factors, it is difficult to avoid the conclusion that the stock market is significantly overvalued.

Many think that low interest rates are one such mitigating factor, though the arguments they make in support of that belief take many guises. Perhaps the best-known is the so-called Fed Model, which became popular in the late 1990s. According to it, the stock market is undervalued whenever equities' earnings yield (the inverse of the P/E ratio) is higher than the yield on the 10-year Treasury. The Fed Model is quite bullish right now, since the S&P 500's earnings yield is 2.6 percentage points above the 10-year Treasury yield (4.6% vs. 2.0%).

History provides precious little support for this model. Over the past 150 years, the earnings yield by itself has a better record when predicting the stock market's subsequent return than does the earnings yield that has been adjusted by prevailing interest rates.

Consider a statistic known as the r-squared, which measures the degree to which one data series (in this case, the earnings yield) explains or predicts another (the stock market's subsequent real, or inflation-adjusted, return). The range of possible r-squared readings is from 0% to 100%, with the former meaning that the indicator has no explanatory ability and the latter indicating complete predictability.

When predicting the market's return over the subsequent decade, for example, the r-squared for the unadjusted earnings yield is 24%. Upon adjusting that yield by the 10-year Treasury yield, the r-squared drops to 10%. The same result emerges when focusing on the cyclically adjusted P/E ratio (CAPE) made famous by Yale University finance professor and Nobel laureate Robert Shiller. (CAPE divides the S&P 500's current level by the average of 10 years of earnings adjusted for inflation.) The r-squared for the CAPE earnings yield by itself is 33%; it drops to 17% when adjusting the CAPE's yield by that of the 10-year Treasury.

The Fed Model fares no better when focusing on predicting the market's subsequent 12-month returns. However, r-squareds are much lower at the one-year horizon, reflecting the greater role luck plays over shorter periods. The r-squared for the earnings yield drops to 1.5% from 1.6% when adjusting for interest rates; for the CAPE yield, the r-squared drops to 4.9% from 5.3%.

To be sure, these results emerge when we automatically assume that lower interest rates are always better for the stock market. Researchers over the years have explored more sophisticated models based on a more nuanced relationship between interest rates and P/E ratios, and some of those models have shown promise. However, those models still suggest that the current stock market is overvalued.

One such model was proposed in a 2017 article in the Journal of Portfolio Management by Research Affiliates founder Robert Arnott and several colleagues. They found that P/E ratios tend to be lower when real interest rates, or those adjusted to remove the effects of inflation, are either too high or too low. The "sweet spot," as far as P/E ratios are concerned, is when real rates are between 3% and 4%. Since real rates currently are below 1%, Mr. Arnott's research provides no support for the above-average current P/E ratio.

In an email, Mr. Arnott poses a rhetorical question for those who believe that today's low interest rates should automatically translate into higher P/E ratios. If that were the case, "then why don't negative real interest rates in Europe and Japan justify even higher valuation levels [than in the U.S.]?! Instead, these markets are priced 20-40% cheaper than the U.S." as judged by their P/E and CAPE ratios, he writes.

The bottom line: You're standing on flimsy ground if you believe today's low interest rates mean that stocks aren't overvalued.

Mr. Hulbert is a columnist whose Hulbert Ratings tracks investment newsletters that pay a flat fee to be audited. He can be reached at reports@wsj.com.